Yazar "Babadağ, Faik" seçeneğine göre listele

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    A new approach to curve couples with Bishop frame
    (Ankara Univ, Fac Sci, 2024) Babadağ, Faik; Atasoy, Ali
    . This paper presents a detailed study of a new generation of the Bishop frame with components including three orthogonal unit vectors, which are tangent vector, normal vector and binormal vector. It is a frame field described on a curve in Euclidean space, which is an alternative to the Frenet frame. It is useful for curves for which the second derivative is not available. Moreover, the conditions which the Bishop frame of one curve coincides with the Bishop frame of another curve are defined. It would be valuable to replicate similar approaches in the Bishop frame of one curve coincides with the Bishop frame of another curve.
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    A New Approach to Fibonacci Tessarines with Fibonacci and Lucas Number Components
    (Adiyaman University, 2021) Babadağ, Faik; Uslu, Merve
    In this paper, by using identities related to the tessarines, Fibonacci numbers and Lucas numbers we define Fibonacci tessarines and Lucas tessarines. We obtain Binet formulae, D’ocagnes identity and Cassini identity for these tessarines. We also give the identities of Fibonacci negatessarines and Lucas negatessarines and define new vector which are called Fibonacci tessarine vector. © 2021, Adiyaman University. All rights reserved.
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    A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors
    (Amer Inst Mathematical Sciences-Aims, 2023) Babadağ, Faik
    This paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented. In addition, a new dual vector called the dual Jacobsthal vector is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of dual space. Finally, this study introduces the dual Jacobsthal and the dual Jacobsthal-Lucas numbers with coefficients of dual numbers. Some fundamental identities are demonstrated, such as the generating function, the Binet formulas, the Cassini's, Catalan's and d'Ocagne identities for these numbers.
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    A new approach to Leonardo number sequences with the dual vector and dual angle representation
    (Amer Inst Mathematical Sciences-Aims, 2024) Babadağ, Faik; Atasoy, Ali
    In this paper, we introduce dual numbers with components including Leonardo number sequences. This novel approach facilitates our understanding of dual numbers and properties of Leonardo sequences. We also investigate fundamental properties and identities associated with Leonardo number sequences, such as Binet's formula and Catalan's, Cassini's and D'ocagne's identities. Furthermore, we also introduce a dual vector with components including Leonardo number sequences and dual angles. This extension not only deepens our understanding of dual numbers, it also highlights the interconnectedness between numerical sequences and geometric concepts. In the future it would be valuable to replicate a similar exploration and development of our findings on dual numbers with Leonardo number sequences.
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    Bicomplex Numbers: Further Contributions to a Fibonacci and Fibonacci - Lucas Matrices Oriented Approach
    (2021) Babadağ, Faik
    In this study, by using Fibonacci Q-matrix and Lucas Q^'-matrix we define bicomplex Fibonacci Q-matrix and bicomplex Lucas Q^'-matrix. After that using this matrix representation, we give some identities.